The present invention relates to a method and system for simplification of the relation between two physiological systems and, more particularly, to simplification of the relation between two physiological systems using system identification techniques.
Physiological Background
It has become a common practice in obstetrics to evaluate the well being of the fetus in utero. This practice, which is known as antepartum testing, has been extensively practiced since the early 1970 on certain high risk obstetrical patients. One of the uses of antepartum testing is to determine how well the placenta is supplying the oxygen and nutrient needs of the growing fetus, and removing fetal wastes therefrom.
Almost 70% of fetal deaths occur before the onset of labor. Antepartum fetal death accounts for nearly 40% of all prenatal mortality in the United States. The majority of fetal deaths occur before 32 week""s gestation.
Antepartum fetal deaths may be categorized into four broad categories: (i) chronic asphyxia of diverse origin; (ii) congenital malformations; (iii) superimposed complications of pregnancy, such as Rhesus isoimmunization, placental abruption, hypertension, diabetes and fetal infection; and (iv) deaths of unexplained cause.
Based on available data, approximately 30% of antepartum fetal deaths may be attributed to asphyxia, 30% to maternal complications, especially placenta abruption, hypertension, and preeclapmsia, 15% to congenital malformations and chromosomal abnormalities, and 5% to infection.
The clinical experience has demonstrated that antepartum fetal assessment can have a significant impact on the frequency and cause of fetal deaths.
Indications for antepartum fetal monitoring in patients known to be at risk of utero-placental insufficiency include maternal, fetal, placental and background indications. Maternal indications include prolonged pregnancy; diabetes mellitus; hypertension and advanced maternal age. Fetal indications include: suspected intrauterine growth restriction (IUGR) and decreased fetal movements. Placental indications include: abruption of the placenta and abnormal amniotic fluid. Background indications include: previous stillbirth.
The fetus and the placenta well being depend upon unique physiological systems responsible at providing an environment capable of supporting fetal growth and development.
To appreciate the complexity of the placenta as a bidirectional transfer organ, it is necessary to point out that the placenta provides the fetus with products which are essential for its well being including essential nutrients, fluids and oxygen, and it serves as a route for clearance of fetal excretory products [Williams Obstetrics, Pritchard and Mc Donald eds., Appleton-Century-Crofts, New York, 1980].
The transport characteristics of the placenta allow respiratory gases and many solutes to reach equal concentration between the maternal intervillous space blood and fetal capillary blood. Thus, the rate of blood flow in these two circulations is important in the determination of fetal oxygen and nutrient supply. Over the course of a normal singleton gestation, uterine blood flow increases more than 50-fold above non-pregnant values. Two factors contribute to this dramatic increase in blood flow: placental growth and maternal arterial vasodilatation.
The uterine artery behaves as a nearly maximally dilated system. Fetal blood flow to the umbilical circulation represents approximately 40% of the fetal cardiac output. During the first trimester, increase in umbilical blood flow is directly proportional to fetal growth.
Many maternal organs undergo physiological changes during the course of pregnancy. Maternal cardiac output, i.e., the product of heart rate and stroke volume, increases by about 30-50% during pregnancy. The distribution of maternal cardiac output changes as pregnancy progresses. In the first trimester the uterus receives about 3% of the cardiac output, however it receives about 17% of the cardiac output near term.
The percentage of cardiac output devoted to kidney, brain and skin is not dramatically altered by pregnancy. Peripheral vascular resistance falls during pregnancy. The cause for this is the smooth muscle relaxing effect of high progesterone levels associated with the pregnancy. There is a progressive rise in venous pressure in the lower extremities.
The placenta, the mother and the fetus make important contribution to the immunological maintenance of pregnancy.
Advances in prenatal and neonatal health care have resulted in a substantial reduction in prenatal and neonatal mortality. These improvements primarily relate to better capabilities in treating maternal diseases during pregnancy, advance in neonatal care and may also be due to improvements in antepartum fetal surveillance techniques.
There are some medical conditions in pregnancy that may lead to poor placental functioning such as diabetes, hypertension, anemia and prolonged pregnancy. In these conditions it is of great importance to evaluate placental functioning. For these or other indications obstetrician will determine whether one is in need to have antepartum testing during the pregnancy.
Antepartum fetal testing is a term that embraces data from fetal movement counts to biophysical monitoring methods, such as contraction stress test, nonstress test, fetal biophysical monitoring profile, amniotic fluid assessment, Doppler velocimetry, vibro-acoustic fetal stimulation and computerized fetal heart rate.
The following lists few of the tests used for fetal monitoring.
Antepartum Fetal Heart Rate Testing (non stress test, NST)
In NST, fetal heart rate acceleration in response to fetal movement are recorded via electronic equipment on a strip of paper.
Cardiotocography (CTG)
CTG utilizes electronic equipment to record the fetus"" heart rate pattern. Uterine contractions, if present, are also registered. This information is recorded on a strip of paper, producing a tracing that is read by the obstetrician. Certain changes in the fetal heart rate pattern can signal a problem.
Amniotic Fluid Index (AFI)
The amount of amniotic fluid surrounding the fetus may be decreased in some high-risk pregnancies. The amount of amniotic fluid present is measured by ultrasound scanning and is known as AFI.
Fetal Biophysical Profile (FBP)
The CTG trace is obtained and then four parameters are observed by ultrasound. The four parameters are fetal tone, fetal movements, fetal breathing, and the amniotic fluid index. Not all of these tests need to be performed at the same time.
Since there are many different pathophysiological processes leading to fetal asphyxia, indication-specific testing is reasonable and it may allow early identification of at-risk fetuses. The FBP is useful in the detection of developing fetal asphyxia even before it irreversible affects the fetus.
No program of antepartum fetal testing can completely remove the risk of fetal death. The most appropriate antepartum tests appear to be amniotic fluid volume assessment, fetal tone and fetal heart monitoring.
The use of Doppler ultrasound is not beneficial in most clinical cases. The single most effective test that distinguishes normal-small from compromised small fetuses is the determination of the umbilical artery Doppler waveform.
Doppler velocimetry seems to be reliable in diagnosing conditions predisposing to IUGR such as chronic hypertension, collagen vascular disorders, and other diseases in which vasospasm plays a major role.
Hence, it remains uncertain which is the optimal Doppler ultrasound measurement of the uteroplacental circulation to obtain the best sensitivity and predictive values for evaluation of fetal and placental pathologies such as preeclampsia and IUGR [Northe R. A., Ferrier C, Long D, Townend K and Pinkus-Smith P. Uterine artery and flow velocity waveforms in the second trimester for the prediction of preeclampcia and fetal growth retardation. Obstetrics and Gynecology Vol 83 pp. 378-386, 1994].
The usual decrease in utheroplacental blood flow associated with uterine contraction, when superimposed with chronic utheroplacental insufficiency (e.g., diabetes associated with vascular changes, postdatism) may result in acute fetal distress.
In contrast, maternal hypotension (e.g., after induction of spinal or epidural anesthesia) can cause acute fetal distress despite the presence of a normal utheroplacental unit. Furthermore, maternal positioning has a strong influence on the condition of the fetus.
There are strong indications that the utheroplacental unit has specific characteristics which can be evaluated by a variety of external manipulations [Gusdon J P Jr, Anderson S G, May W J. A clinical evaluation of the xe2x80x9croll-over testxe2x80x9d for pregnancy induced hypertension. Am J obstet Gynecol 1: 127(1): 1-3, January 1997; Eneroth-Grimforms E, Bevegard S, Nilsson Ba. Evaluation of three simple physiological tests as predictors of pregnancy-induced hypertension. A pilot study. Acta Obstet Gynecol Scand; 67(2):109-113, 1988; Peck T M A simple test for predicting pregnancy-induced hypertension. Obstet Gynecol 50(5):615-617 November 1977; Andersen G J. The roll over test as a screening procedure for gestational hypertension. Aust N Z J Obstet Gynecol 20(3): 144-150, August 1980; Baker P N, Johnson I R. The use of the hand-grip test for predicting pregnancyxe2x80x94induced hypertension. Eur J Obstet Gynecol Reprod Biol 56(3):169-172, September 1994; Degani S, Abinader E, Eibschitz I, Oettinger M, Shapiro I, Sharf M. Isometric exercise test for predicting gestational hypertension. Obstet Gynecol 65(5):652-654, May 1985; Loyke H F. Cold pressor test as a predictor of the severity of hypertension. Sounth Med J ; 88(3):300-304, May 1995; Chang C, Zhang J. The analysis of relationship between fetal stress and blood dynamics in fetal vessels and placenta bed vessels. Chung Hau Fu Vhan Tsa Chin 31(1)46:15-17, January 1996; Cottrill C M, Jeffers Lo J, Ousey J C, McGladdery A J, Ricketts S W, Silver M, Rossdale PD. The placenta as a determinant of fetal well being in normal and abnormal pregnancies. J. Reproduct Fertil Suppl 44:591-601, 1991; Fairlie F M. Doppler flow velocimetry in hypertension in pregnancy. Clin Perinatol 18(4):749-778, December 1991; Badalian S S. Nature and mechanism of hemodynamic changes in fetuses of mothers with various types of diabetes mellitus. Akush Ginekol Mosk 9:39-42, September 1989.
There is no doubt that better objective and advanced measures of placenta well being and fetal asphyxia and asphyxia-related morbidity are needed to allow for a more scientific approach of antenatal fetal surveillance.
Mathematical Background
Modulation and Demodulation
The modulation process combines a narrowband signal, s(t), with a signal of higher frequency (relative to the frequency band of s(t)). Modulating a high frequency signal (known as the carrier, c(t)) is advantageous since low frequency signals cannot be transmitted through most media. For example, transmitting a speech signal, with frequencies of 300-4000 Hz as a radio signal is highly difficult but after modulating it on a 100 MHz carrier, the task becomes much easier. A second advantage of modulation is the ability, using numerous carriers, to transmit many signals with the same basic frequencies without interference. Demodulation is the complementary process of extracting the narrowband signal, s(t), from the carrier, c(t). A common modulation scheme is the Amplitude Modulation (AM) [Couch L. W. Digital and Analog Communication Systems. 5th ed., 1997 Prenctice-Hall Jew-Jersey]:
r(t)=Axc2x7(1+mxc2x7s(t))sin(2xcfx80fct)
where r(t) is the transmitted signal; A is the amplitude of the transmitted signal; m is the modulation index and ranges between 0 and 1; s(t) is the modulating signal containing the information; and fc is the frequency of the carrier.
A similar modulation scheme is the Double-Sideband Suppressed Carrier (DSB-SC). This modulation resembles an amplitude modulation with suppressed carrier [Couch L. W. Digital and Analog Communication Systems. 5th ed., 1997 Prenctice-Hall Jew-Jersey]:
r(t)=Axc2x7s(t)xc2x7sin(2xcfx80fct)
Usually it is assumed that the modulating signal, s(t), has no DC component.
Another common modulation scheme is the Frequency Modulation (FM) [Couch L. W. Digital and Analog Communication Systems. 5th ed., 1997 Prenctice-Hall Jew-Jersey]:       r    ⁡          (      t      )        =      A    ⁢          xe2x80x83        ⁢    sin    ⁢          xe2x80x83        ⁢          (                        2          ⁢                      xe2x80x83                    ⁢          π          ⁢                      xe2x80x83                    ⁢                      f            c                    ⁢          t                +                  β          ⁢                      xe2x80x83                    ⁢                                    ∫                              -                ∞                            t                        ⁢                                          s                ⁡                                  (                  τ                  )                                            ⁢                              ⅆ                τ                                                        )      
where xcex2 is the maximal frequency shift.
The instantaneous frequency of the carrier equals a constant plus the modulating signal. A closely related modulation scheme is the Phase Modulation (PM) in which the phase of the carrier is the modulating signal [Couch L. W. Digital and Analog Communication Systems. 5th ed., 1997 Prenctice-Hall Jew-Jersey]:
r(t)=A sin(2xcfx80fct+xcex2s(t))
Modulation of information of high frequency carriers can occur from natural processes also. For example, a transmitted ultrasound signal is reflected from a moving tissue with a small frequency shift which is known as the Doppler shift. This shift, which is proportional to the velocity of the reflecting tissue, can be extracted from the incoming ultrasound signal using conventional FM demodulation techniques.
System Identification Techniques
A system is an object in which different kind of variables interact and produce observable signals [Ljung L. System Identification; theory for the user. Prentice-Hall Inc., Englwood Cliffs, N.J. Edited by T. Kailath, 1987]. The observable signals that are of interest are usually referred to as xe2x80x9coutputsxe2x80x9d. The system is also affected by external stimuli. External signals that can be manipulated by the observer are referred to as xe2x80x9cinputsxe2x80x9d. Others are referred to as xe2x80x9cdisturbancesxe2x80x9d and can be divided into those that are directly measured and those that are only observed through their influence on the output. The distinction between inputs and measured disturbances is often less important for the modeling process.
Clearly, the notion of a system is a broad concept and plays an important role in modern science. Dynamic systems are those for which the current output value depends not only on the current external stimuli but also on earlier values.
When one interacts with a system, one needs to have a concept of how the system""s variables relate to one another. With a broad definition, the relationship among observed signals is referred to as xe2x80x9ca model of the systemxe2x80x9d. Models can come in various shapes with varying degree of mathematical formalism. The intended use determines the degree of sophistication that is required to make the model purposeful.
Mathematical models describe the relationship among system variables in terms of mathematical expressions like difference or differential equations. Mathematical models may be characterized by a number of adjectives (time continuous or time discrete, lumped or distributed, deterministic or stochastic, linear or nonlinear, etc.) signifying the type of differential equation used.
Basically, a model has to be constructed from observed data. Mathematical models may be developed along two routs.
One route is to split the system into subsystems, whose properties are well understood from previous experience. These subsystems are then joined mathematically and a model of the whole system is obtained. This route is known as xe2x80x9cModelingxe2x80x9d, and does not necessarily involve any experimentation on the actual system.
The other route to mathematical as well as graphical models is directly based on experimentation. Input and output signals from the system, are recorded and subjected to data analysis in order to infer a model. This route is known as xe2x80x9cSystem Identificationxe2x80x9d, the final outcome of which is a model of the system under study.
System identification is the subject of constructing or selecting models of dynamic systems to serve certain purposes. A first step is to determine a class of models within which the search for the most suitable model is to be conducted. A model of a system is a description of its properties, suitable for a certain purpose. The model need not be a true and accurate description of the system, nor need the user believe it to be so, in order to serve its purpose.
Quiet often it is not possible to determine, apriori, the coefficients characterizing the system from knowledge of the physical mechanisms that govern the system""s behavior. Instead, the determination of all or some of them must be left to estimation procedures. The model thus becomes a set of models and it is for the estimation procedure to select that member in the set that appears to be the most suitable for the purpose in question.
The procedure to determine a model of a dynamic system from observed input-output data involves four basic ingredients [Ljung L. System Identification; theory for the user. Prentice-Hall Inc., Englwood Cliffs, New Jersy. Edited by T. Kailath, 1987]:
1. The data: The input-output data which are recorded during a specific designed identification procedure.
2. A set of candidate models: A set of candidate models is obtained by specifying within which collection of models one is going to look for a suitable one.
3. A rule by which candidate models can be assessed using the data: This is the identification method, and is based on the performance of the model when one attempts to reproduce the measured data. A deficient model in these respects makes one reject the model, while good performance will develop a certain confidence in the model.
4. The procedure of identification is repeated for nonoverlapping segments of each set of data, in order to evaluate the accuracy of the model and the confidence level of the results.
However, a model can never be regarded as a final and true description of the system. It can at best be regarded as a good enough description of certain aspects of particular interest.
Several system identification models are known in the art, such as, for example, nonparametric models, parametric models, polynominal representation, simple autoregressive model, ARMAX model structure, output error structure, Box-Jenkins model structure, general parametric model structure, state space representation, linear time-varying models, time-invariant model, nonlinear models, nonlinear ARMAX, Wiener kernels model, Korenberg-Billings model and Volterra-Wiener model.
The present invention is based on the broad concept of system identification, using the relationship between mother and fetus as an input-output open-loop system connected by a connection function. System identification deals with the problem of building mathematical models of dynamic systems, based on observed data. The area has matured into an established collection of basic techniques that are well understood and known to be successfully performed in practical applications. Since the mother and fetus are connecting solely via the placenta, the present invention enables placental and fetal functionality assessment.
There is thus a widely recognized need for, and it would be highly advantageous to have, a method and system for evaluating the condition of the placenta in pregnant women as well as the well being of the fetus by using physiological parameters and system identification methods.
According to one aspect of the present invention there is provided a method of determining the well being of a placenta in a pregnant woman having a maternal-placenta-fetal system, the method comprising the steps of (a) simultaneously monitoring selected maternal and fetal physiological signals; (b) preprocessing the maternal and fetal physiological signals by independently non-linearly or linearly mathematically decomposing the maternal and fetal physiological signals into mathematical constituents thereof and collecting constituents of the mathematical constituents having a highest degree of linearity and/or simplicity; (c) using the constituents having the highest degree of linearity and/or simplicity for identifying a mathematical model describing the maternal-placenta-fetal system, and mathematical parameters describing the model; and (d) determining, according to the mathematical model and the mathematical parameters describing the mathematical model, the well being of the placenta.
According to another aspect of the present invention there is provided a method of determining the well being of a fetus in a pregnant woman having a maternal-placenta-fetal system, the method comprising the steps of (a) simultaneously monitoring selected maternal and fetal physiological signals; (b) preprocessing the maternal and fetal physiological signals by independently non-linearly or linearly mathematically decomposing the maternal and fetal physiological signals into mathematical constituents thereof and collecting constituents of the mathematical constituents having a highest degree of linearity and/or simplicity; (c) using the constituents having the highest degree of linearity and/or simplicity for identifying a mathematical model describing the maternal-placenta-fetal system, and mathematical parameters describing the model; and (d) determining, according to the mathematical model and the mathematical parameters describing the mathematical model, the well being of the fetus.
According to yet another aspect of the present invention there is provided a method of determining a maternal-fetus relation in a pregnant woman having a maternal-placenta-fetal system, the method comprising the steps of (a) simultaneously monitoring selected maternal and fetal physiological signals; (b) preprocessing the maternal and fetal physiological signals by independently non-linearly or linearly mathematically decomposing the maternal and fetal physiological signals into mathematical constituents thereof and collecting constituents of the mathematical constituents having a highest degree of linearity and/or simplicity; (c) using the constituents having the highest degree of linearity and/or simplicity for identifying a mathematical model describing the maternal-placenta-fetal system, and mathematical parameters describing the model; and (d) determining, according to the mathematical model and the mathematical parameters describing the mathematical model, the maternal-fetus relation.
According to still another aspect of the present invention there is provided a system for monitoring a pregnancy in a pregnant woman having a maternal-placenta-fetal system, the system comprising (a) at least one monitoring device simultaneously monitoring selected maternal and fetal physiological signals; and (b) a computerized system being in communication with each of the at least one monitoring device for preprocessing the maternal and fetal physiological signals by independently non-linearly or linearly mathematically decomposing the maternal and fetal physiological signals into mathematical constituents thereof and collecting constituents of the mathematical constituents having a highest degree of linearity and/or simplicity, and for using the constituents having the highest degree of linearity and/or simplicity for identifying a mathematical model describing the maternal-placenta-fetal system, and mathematical parameters describing the model.
According to further features in preferred embodiments of the invention described below, while simultaneously monitoring the selected maternal and fetal physiological signals the pregnant woman is provoked by an external stimulus.
According to still further features in the described preferred embodiments the physiological signals are selected from the group consisting of ECG, BP, PO2, PCO2, blood flow, blood velocity, blood volume, thermal index and respiration.
According to still further features in the described preferred embodiments the mathematical model is selected from the group consisting of nonparametric models, parametric models, polynominal representation, simple autoregressive model, ARMAX model structure, output error structure, Box-Jenkins model structure, general parametric model structure, state space representation, linear time-varying models, time-invariant model, nonlinear models, nonlinear ARMAX, Wiener kernels model, Korenberg-Billings model and Volterra-Wiener model.
According to still further features in the described preferred embodiments the step of identifying the mathematical model is effected by identifying a best mathematical model describing the maternal-placenta-fetal system, the best mathematical model is selected out of a plurality of available mathematical models and according to predetermined criteria.
According to still further features in the described preferred embodiments the model is a linear model.
According to still further features in the described preferred embodiments the step of preprocessing the maternal and fetal physiological signals includes at least one process selected from the group consisting of (i) calculating a maternal heart rate from an inter-beat interval of maternal ECG; (ii) calculating maternal heart rate from maxima values of maternal blood flow; (iii) calculating a maternal pulse wave velocity from a delay between R-waves of an ECG and corresponding systoles of blood flow signal; (iv) calculating maternal contractility from maternal blood flow by determining maximal derivative in a maternal systole stage; (v) calculating a fetal heart rate from an inter-beat interval of fetal ECG; (vi) calculating a fetal heart rate from an inter-beat interval of fetal Doppler signal representing fetal heart valve closing; (vii) calculating a fetal blood flow using ultrasound reflection from a fetal blood vessel; (viii) calculating a fetal heart rate from fetal blood flow rate; and (ix) calculating a fetal blood flow rate using ultrasound reflection from a fetal blood vessel.
The present invention successfully addresses the shortcomings of the presently known configurations by providing a method and system for evaluating the condition of the placenta in pregnant women as well as the well being of the fetus by using physiological parameters and system identification methods.
Implementation of the method and system for evaluating the condition of the placenta in pregnant women as well as the well being of the fetus by using physiological parameters and system identification methods involves performing or completing selected tasks or steps manually, automatically, or a combination thereof Moreover, according to actual instrumentation and equipment of preferred embodiments of the method and system of the present invention, several selected steps could be implemented by hardware or by software on any operating system of any firmware or a combination thereof. For example, as hardware, selected steps of the invention could be implemented as a chip or a circuit. As software, selected steps of the invention could be implemented as a plurality of software instructions being executed by a computer using any suitable operating system. In any case, selected steps of the method and system of the invention could be described as being performed by a data processor, such as a computing platform for executing a plurality of instructions.